I would suggest looking at Premier Inns, which, as Claudia noted, is a chain of hotels throughout the UK. I have stayed in them in various locations and have always been pleased. They are consistently clean, comfortable (great beds!), and very reasonably priced; especially for London. They have them all over London, so it's easy to find one in a convenient place. Breakfast is available but costs extra (although the price is good for what you get).
I recently stayed at the Premier Inn County Hall, which had the advantage of being within walking distance of the Westminster area, and many other places. But it was also convenient to places like Borough Market, which has such good food and interesting things. The Premier Inn Paddington Station is the newest PI, and is right next to the Paddington station, which can be helpful for local transport. There are plenty of others in central London, but I would strongly suggest that you book as soon as you can, as the price goes up the closer you get.